MATLAB Mathematics - SERC - Index of

Initial Value Problems for ODEs and DAEs
(t,y) for µ = MU. The use of an analytic Jacobian can improve the reliability
and efficiency of integration.
To run this example, click on the example name, or type vdpode at the
command line. From the command line, you can specify a value of µ as an
argument to vdpode. The default is µ = 1000.
function vdpode(MU)
%VDPODE Parameterizable van der Pol equation (stiff for large MU)
if nargin < 1
MU = 1000; % default
end
tspan = [0; max(20,3*MU)];
y0 = [2; 0];
options = odeset('Jacobian',@J);
% Several periods
[t,y] = ode15s(@f,tspan,y0,options);
plot(t,y(:,1));
title(['Solution of van der Pol Equation, \mu = ' num2str(MU)]);
xlabel('time t');
ylabel('solution y_1');
axis([tspan(1) tspan(end) -2.5 2.5]);
---------------------------------------------------------------
function dydt = f(t,y)
dydt = [
y(2)
MU*(1-y(1)^2)*y(2)-y(1) ];
end % End nested function f
---------------------------------------------------------------
function dfdy = J(t,y)
dfdy = [ 0 1
-2*MU*y(1)*y(2)-1 MU*(1-y(1)^2) ];
end % End nested function J
end
5-21